Abstract:
In this talk, we will review fast multipole methods (FMMs) and tree methods, which reduce the computational complexity of solving the boundary integral form of many partial
differential equations. We will review the general formulation and execution of an FMM, variations and complications when applied to PDEs with oscillatory Green's functions, and a novel formulation of the high-frequency Helmholtz FMM that accelerates some
of the time-critical stages of the algorithm. This Fourier-based Helmholtz FMM makes the interpolation steps fast and accurate, retains the diagonality of the transfer function, and provides a simplified, a priori error analysis. Time permitting, recent results
on applying GPU computing to generalized formulations of the FMM and related problems will be shown.
Bio:
Cris Cecka joined the Institute for Applied Computational Science in July as a Lecturer and researcher. This academic year, he is teaching CS205 - Computing Foundations of Computational Science and CS207
- Systems Development for Computational Science. For research, he works with Hanspeter Pfister's Visual Computing Lab and is developing collaborative research with Boston University, the University of Massachusetts, and IBM. Cecka's research combines topics
in high-performance computing, computational physics, and applied mathematics. His research focus includes the development of novel fast multipole methods for applications in boundary element formulations, high performance computing with GPUs, and applications
of GPU computing for finite element and boundary element methods. He received his Ph.D. in Computational Mathematics in 2011 from Stanford University and degrees in physics and joint computer science/math from Harvey Mudd College in 2006.